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IET Information Security

Efficient module learning with errors‐based post‐quantum password‐authenticated key exchange

Peixin Ren, Xiaozhuo Gu, Ziliang Wang

Published Sep 20, 2022• 16 citations
Publisher

Abstract

Abstract Password‐authenticated key exchange ( PAKE ) is a cryptographic primitive that can establish secure remote communications between the client and the server, especially with the advantage of amplifying memorable passwords into strong session keys. However, the arrival of the quantum computing era has brought new challenges to traditional PAKE protocols. Thus, designing an efficient post‐quantum PAKE scheme becomes an open research question. In this paper, the authors construct a quantum‐safe PAKE protocol, which is a horizontal extension of the password‐authenticated key (PAK) protocol in the field of module lattices. Subsequently, the authors accompany the proposed protocol with a rigorous security proof in the random oracle model with two adaptions: applying the CDF‐Zipf model to characterise the ability of the adversary and using the pairing with errors assumption to simplify the proof. Taking the flexibility of the module learning with errors ( MLWE ) problem, the authors elaborately select three parameter sets to meet different application scenarios. Specifically, the authors’ Recommended‐PAKE implementation achieves 177‐bit post‐quantum security with a generous margin to cope with later improvement in cryptanalysis. The performance results indicate that the authors’ MLWE‐PAKE is quite practical: compared with the latest Yang‐PAK , the authors’ Recommended‐PAK reduces the communication cost and the running time by 36.8% and 13.8%, respectively.

DOI
10.1049/ise2.12094

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IEEE Access•Jan 1, 2023•35 citations
Abstract Password‐authenticated key exchange ( PAKE ) is a cryptographic primitive that can establish secure remote communications between the client and the server, especially with the advantage of amplifying memorable passwords into strong session keys. However, the arrival of the quantum computing era has brought new challenges to traditional PAKE protocols. Thus, designing an efficient post‐quantum PAKE scheme becomes an open research question. In this paper, the authors construct a quantum‐safe PAKE protocol, which is a horizontal extension of the password‐authenticated key (PAK) protocol in the field of module lattices. Subsequently, the authors accompany the proposed protocol with a rigorous security proof in the random oracle model with two adaptions: applying the CDF‐Zipf model to characterise the ability of the adversary and using the pairing with errors assumption to simplify the proof. Taking the flexibility of the module learning with errors ( MLWE ) problem, the authors elaborately select three parameter sets to meet different application scenarios. Specifically, the authors’ Recommended‐PAKE implementation achieves 177‐bit post‐quantum security with a generous margin to cope with later improvement in cryptanalysis. The performance results indicate that the authors’ MLWE‐PAKE is quite practical: compared with the latest Yang‐PAK , the authors’ Recommended‐PAK reduces the communication cost and the running time by 36.8% and 13.8%, respectively.
The Password-Authenticated Key Exchange (PAKE) protocol is a useful tool for establishing secure remote communication between users, especially given the prevalence of amplifying a human-memorable password into a strong session key in the age of hand-held devices. Recent advances in quantum computing have stimulated interest in quantum-safe cryptographic schemes. Therefore, we propose QSPAK and QSPPK, two post-quantum and efficient PAKE protocols which are parallel extensions of PAK and PPK, but based on the hardness assumption over module lattices. Specifically, we make a comprehensive trade-off among multiple significant performance indicators such as the post-quantum security, the failure rate, the communication cost and the running time to guide optimal parameter choices. This rigorous instantiation has never been seen in previous PAKE papers. Additionally, utilizing the flexibility of module lattices, we provide three parameter sets (#1, #2, and #3) matching different security scenarios. We implement and benchmark QSPAK and QSPPK against other competitive proposals. The performance results indicate that our QSPAK and QSPPK, besides being more efficient, exhibit the flexibility and security advantages over the latter schemes. Furthermore, we construct a post-quantum password-authenticated TLS 1.3 framework, aimed towards provide a further suggestion for IETF standardization of quantum-safe PAKE.
An authenticated mobile key exchange is necessary for post quantum secure communication over a public channel. It allows two entities to create a secure and unique session key for every communication session. We feel a need to design two party efficient and secure authenticated key agreement. We have also observed all the protocols given above are based on learning with error assumption over a finite ring. The ”Module Learning with Errors” assumption is the more appropriate choice among ”Learning with Errors” and ”Ring Learning with Errors” for designing practical password-authenticated key exchange protocols. With the help of ”Module Learning with Errors” assumption, and by lowering the number of ring polynomials, several implementations of the protocols can be realized. Therefore, this paper contains quantum safe, efficient, and practical ”Module Learning with Errors” assumption based authenticated key agreement protocol. The protocol’s security analysis is presented within the framework of the random oracle model.
Password authentication is a prevalent method of user verification across the Internet, and its use extends to scenarios where resources are limited. However, current password authentication protocols primarily rely on traditional password authenticated key exchange (PAKE) protocols (e.g., SRP, OPAQUE), which are vulnerable to attacks by quantum adversaries. To date, no efficient quantum algorithm has been found to solve the common challenges in lattice-based cryptography. Therefore, quantum-resistant PAKE protocols are generally built upon lattice-based cryptography. In this work, we propose a threshold verifiable oblivious pseudorandom function () protocol based on secret sharing. We then integrate it into a PAKE protocol and present an instantiation of a quantum-safe threshold PAKE protocol () based on the Ring Learning with Errors (RLWE) assumption. This integration gives our PAKE protocol resistance to precomputation attacks, similar to OPAQUE. Furthermore, by incorporating thresholding techniques into the PAKE protocol, we mitigate the risk of single points of failure on the server side. Our protocol not only preserves the security guarantees of traditional PAKE schemes but also resists attacks from quantum adversaries. We also provide a comprehensive security analysis and evaluation of, providing valuable insights for its practical implementation.
Secure Remote Password (SRP) protocol is an essential password-authenticated key exchange (PAKE) protocol based on the discrete logarithm problem (DLP). The protocol is specifically designed to obtain a session key and it has been widely used in various scenarios due to its attractive security features. In the SRP protocol, the server is not required to save any data directly associated with passwords. And this makes attackers who manage to corrupt the server fail to impersonate the client unless performing a brute-force search for the password. However, the development of quantum computing has potentially made classic DLP-based public-key cryptography schemes not secure, including the SRP protocol. So it is significant to design a quantum-resistant SRP protocol. In this paper, based on the original scheme, we propose a post-quantum SRP protocol from the learning with errors (LWE) problem. And we give rigorous proof and analyses on the correctness and security of the scheme. Besides being resistant to known quantum attacks, it maintains the various secure qualities of the original protocol.
Stronger anonymity password authentication key exchange protocols based on traditional cryptography are not resistant to quantum computing attacks, and there is no lattice-only anonymous password authentication key exchange protocol protocol that satisfies the strong anonymity requirement. Therefore, this paper constructs stronger anonymity PAKE protocol based on the ring learning with errors (RLWE) and smooth projective hash function (SPHF) based on ideal lattice. The proposed protocol can achieve stronger anonymity and resists to desynchronization attacks and quantum attack. The security of the protocol is proved under the BPR model. The security and performance analysis shows that the proposed PAKE protocol has better advantages in security and efficiency.
A three-party authenticated key exchange protocol enables two entities to agree on a session key with the help of a dedicated server over public channel. Shor’s algorithm is a big threat for existing authenticated key exchange protocols. Lattice based cryptography plays a very important role in designing authentication and key agreement secure against the threat of quantum attacks. However, it is not easy job to design quantum resistant password based three party protocol due to the high demand for security requirements and the limited resources nature of mobile devices. In this article, we have proposed a new post quantum three party key exchange based on ring learning with errors assumption. This protocol is motivated from Islam et al.’s authenticated key exchange protocol. Their protocol is not secure against stolen smartcard attack, password guessing attack, and can’t provide user anonymity. The anonymous communication is a big requirement for practical applications like e-healthcare services/smart vehicular communication. This paper also contains the performance analysis of the proposed protocol along with other relevant protocols.